AC Signal Amplitude Modulation in Resonant Tank Circuit

[HMS-776]

I recently simulated a parallel resonant tank circuit on multisim.

I put an oscope across the tank circuit and I get an AC signal, but what interests me is that it is amplitude modulated. The oscillations slowly build up in amplitude, hit a peak and then die back down.

I think that the increased amplitude is due to the inductor and capacitor charging, once they hit their peak charge no more energy is input from the source and the energy begins to slowly dissipate...Until it reaches a point where it begins to charge again...Is this close at all to what is going on?

Can anyone explain to me why the AC signal has amplitude modulation?

 

[waht]

Does the circuit have a power source somewhere, AC or DC?

 

[HMS-776]

Input is pulsed DC (square wave) from the secondary coil of a transformer.

 

[waht]

That kind of explains it. A square wave can be Fourier decomposed into an infinite sum of sinusoids with odd order frequencies. So you could write,

$$sqw(t) = cos(\omega t) - cos(3\omega t)/3 + cos(5\omega t)/5 ...$$

Also, an LC parallel tank circuit acts as a bandpass filter. It's properties, such as a center frequency or the bandwidth depends on the values of L and C. So what's happening is you are filtering out some of the harmonics of the square wave.

Here is a W|A plot of a square wave approximation: http://www.wolframalpha.com/input/?i=plot+cos(x)+-+cos(3x)/3+++cos(5x)/5+-+cos(7x)/7"

Here is another plot showing what happens when some cosine terms are removed because of being filtered out: http://www.wolframalpha.com/input/?i=plot++cos(5x)/5+-+cos(7x)/7"

Depending on the parameters such as the frequency of the square wave or values of L and C, you can get different outputs.

 

[skeptic2]

How does the time step of your simulation compare to the resonant frequency?